Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, n\neq 0$. $\dfrac{{pn^{-4}}}{{(p^{-5}n^{3})^{-5}}}$
Answer: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${pn^{-4} = pn^{-4}}$ On the left, we have ${p}$ to the exponent ${1}$ . Now ${1 \times 1 = 1}$ , so ${p = p}$ Apply the ideas above to simplify the equation. $\dfrac{{pn^{-4}}}{{(p^{-5}n^{3})^{-5}}} = \dfrac{{pn^{-4}}}{{p^{25}n^{-15}}}$ Break up the equation by variable and simplify. $\dfrac{{pn^{-4}}}{{p^{25}n^{-15}}} = \dfrac{{p}}{{p^{25}}} \cdot \dfrac{{n^{-4}}}{{n^{-15}}} = p^{{1} - {25}} \cdot n^{{-4} - {(-15)}} = p^{-24}n^{11}$